Problem: Rewrite as a simplified fraction. ${2.3\overline{1} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 231.1111...\\ 10x &= 23.1111...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 208}$ ${x = \dfrac{208}{90}} $ ${x = \dfrac{104}{45}} \text{or} {2 \dfrac{14}{45}}$